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Related papers: On Stochastic Comparisons of Order Statistics from…

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We determine the joint limiting distribution of adjacent spacings around a central, intermediate, or an extreme order statistic $X_{k:n}$ of a random sample of size $n$ from a continuous distribution $F$. For central and intermediate cases,…

Statistics Theory · Mathematics 2017-02-21 H. N. Nagaraja , Karthik Bharath , Fangyuan Zhang

In this paper, higher-order expansions for distributions and densities of powered extremes of standard normal random sequences are established under an optimal choice of normalized constants. Our findings refine the related results in Hall…

Probability · Mathematics 2016-01-05 Wei Zhou , Chengxiu Ling

In reliability and life testing studies, the topic of estimating hazard rate has received great attention in recent years since an estimate of hazard rate is a quite useful tool for making decisions. Some works have included nonparametric…

Statistics Theory · Mathematics 2012-05-24 Baris Surucu

Let $\{X_{n}, n\ge 1\}$ be a sequence of independent random variables with common general error distribution $GED(v)$ with shape parameter $v>0$, and let $M_{n,r}$ denote the $r$th largest order statistics of $X_{1}, X_{2}, \cdots, X_{n}$.…

Probability · Mathematics 2019-05-07 Yingyin Lu , Zuoxiang Peng

We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence order that is defined for two random variables to the case $n>2$. All conventional stochastic orders are…

Applications · Statistics 2018-12-11 Maxim Finkelstein , Nil Kamal Hazra

A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of…

Risk Management · Quantitative Finance 2010-10-26 Georg Mainik , Ludger Rüschendorf

In this work, we establish some stochastic comparison results for multivariate skew-elliptical random vectors. These multivariate stochastic comparisons involve Hessian and increasing-Hessian orderings as well as many of their special…

Statistics Theory · Mathematics 2023-04-19 Chuancun Yin

Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…

Risk Management · Quantitative Finance 2024-02-26 Alois Pichler

Stochastic comparisons of series and parallel systems are important in many areas of engineering, operations research and reliability analysis. These comparisons allow for the evaluation of the performance and reliability of systems under…

Statistics Theory · Mathematics 2025-06-09 CM Revathi , Rajesh Moharana , Raju Bhakta

In this paper we provide a novel family of stochastic orders that generalizes second order stochastic dominance, which we call the $\alpha,[a,b]$-concave stochastic orders. These stochastic orders are generated by a novel set of "very"…

Probability · Mathematics 2021-04-28 Bar Light , Andres Perlroth

This note describes non-asymptotic variance and tail bounds for order statistics of samples of independent identically distributed random variables. Those bounds are checked to be asymptotically tight when the sampling distribution belongs…

Probability · Mathematics 2012-11-05 Stephane Boucheron , Maud Thomas

Let $X_1, X_2,\ldots, X_n$ be $n$ independent and identically distributed random variables, here $n \geq 2.$ Let $X_{(1)}, X_{(2)}, \ldots, X_{(n)}$ be the order statistics of $X_1, X_2,..., X_n.$ In this note we proved that: (I) If $X_1,…

Statistics Theory · Mathematics 2015-03-04 Robert W. Chen

A characterization of the exponential distribution based on equidistribution conditions for maxima of random samples with consecutive sizes n-1 and n for an arbitrary and fixed n>2 is proved. This solves an open problem stated recently in…

Probability · Mathematics 2015-02-24 Santanu Chakraborty , George P. Yanev

In this work, we consider two sets of dependent variables $\{X_{1},\ldots,X_{n}\}$ and $\{Y_{1},\ldots,Y_{n}\}$, where $X_{i}\sim EW(\alpha_{i},\lambda_{i},k_{i})$ and $Y_{i}\sim EW(\beta_{i},\mu_{i},l_{i})$, for $i=1,\ldots, n$, which are…

Other Statistics · Statistics 2024-12-18 Ramkrishna Jyoti Samanta , Sangita Das , N. Balakrishnan

In this article, we focus on stochastic orders to compare the magnitudes of two parallel systems from Weibull distributions when one set of scale parameters majorizes the other. The new results obtained here extend some of those proved by…

Statistics Theory · Mathematics 2021-02-19 Nuria Torrado , Subhash C. Kochar

In this paper, we consider finite mixture models with modified proportional hazard rates. Sufficient conditions for the usual stochastic order and the hazard order are established under chain majorization. We study stochastic comparisons…

Statistics Theory · Mathematics 2024-07-24 Lina Guo

If the hazard rate $ \frac{ F'(x) }{ 1-F(x) } $ is increasing (in $x$), then $ \mathbb E\, ( X_{n:n} - X_{n-1:n} ) $ is decreasing (in $n$), and moreover, completely monotone.

Probability · Mathematics 2019-11-19 Boris Tsirelson

Most of the stochastic orders for comparing random variables, considered in the literature, are afflicted with two main drawbacks: (i) lack of connex property and (ii) lack of consideration of any dependence structure between the random…

Methodology · Statistics 2021-03-03 Sugata Ghosh , Asok K. Nanda

Let $\{X_{1},\ldots,X_{N_1}\}$ and $\{Y_{1},\ldots,Y_{N_2}\}$ be two sequences of interdependent heterogeneous samples, where for $i=1,\ldots,N_{1},$ $X_{i}\sim \text{Kw-G}(x, \alpha_{i}, \gamma_{i};G)$ and for $i=1,\ldots,N_{2},$…

Statistics Theory · Mathematics 2025-08-21 Sangita Das , Narayanaswamy Balakrishnan

An extension of Archimax copula class in more than two random variables ( Multivariate ) was introduced in (J\'agr 2011) for describing dependency structures among random variables in higher dimension, and some properties of Archimax copula…

Statistics Theory · Mathematics 2024-02-06 Sarikul Islam , Nitin Gupta